Question

The tires on your truck have 0.35 m radius. In a straight line, you drive 2600 m. What is the angular displacement of the tire, during this trip? Would the angular displacement be more or less if you put on big mud tires with a radius of .60m

Mud tires have (more or less) angular displacement

Answer 1

7420.4 radian (approximately)

Mud tires have less angular displacement

Step-by-step explanation

Given that,

The total distance covered = 2600 m

circumference of the wheel

2 π r

2 * 3.14 * 0.35m

= 2.20m

number of rotations of the wheel

2600 / 2.20

= 1181.81

≈ 1181

1 rotation the angular displacement ---> 2π (radian)

1181 rotation the angular displacement ---> 2π * 1181

= 7420.4 radian(approximately)

Angular displacement is directly proportional to number of rotation.

So,

angular displacement = 2600 / 2 π r

so it can be seen that angular displacement is indirectly proportional to radius, means more the radius less will be angular displacement.